Type a molecules are kazhdan-lusztig

Michael S Chmutov

Research output: Contribution to journalConference article

1 Scopus citations

Abstract

Let (W; S) be a Coxeter system. A W-graph is an encoding of a representation of the corresponding Iwahori-Hecke algebra. Especially important examples include the W-graph corresponding to the action of the Iwahori-Hecke algebra on the Kazhdan-Lusztig basis as well as this graph's strongly connected components (cells). In 2008, Stembridge identified some common features of the Kazhdan-Lusztig graphs ("admissibility") and gave combinatorial rules for detecting admissibleW-graphs. He conjectured, and checked up to n = 9, that all admissible An-cells are Kazhdan-Lusztig cells. The current paper provides a possible first step toward a proof of the conjecture. More concretely, we prove that the connected subgraphs of An-cells consisting of simple (i.e. directed both ways) edges do fit into the Kazhdan-Lusztig cells.

Original languageEnglish (US)
Pages (from-to)313-324
Number of pages12
JournalDiscrete Mathematics and Theoretical Computer Science
StatePublished - Nov 18 2013
Event25th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2013 - Paris, France
Duration: Jun 24 2013Jun 28 2013

Keywords

  • Dual equivalence graphs
  • Iwahori-hecke algebra
  • Kazhdan-lusztig cells
  • W-graphs
  • W-molecules

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